The market price of JS stock is currently $30. It is known that at the end of three months it will be either $33 or $27. The risk-free interest rate is 8% per annum with continuous compounding.

(a) Use a one-step binomial tree to calculate the value of a three-month European put option on the JS stock with a strike price of $31? Use no-arbitrage arguments (you need to show how to set up the riskless portfolio).

(b) Use the same one-step binomial tree and your results from (a) to determine the price of a three-month American put option on the JS stock with a strike price of $31